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Recent questions tagged vectoranalysis
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GATE2020EC: 1
If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$? It is not necessary that these vectors span $\mathbb{R}^{4}$ ... $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.
asked
Feb 13
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by
jothee
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1.4k
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gate2020ec
vectoranalysis
engineeringmathematics
0
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0
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2
GATE2020EC: 24
The random variable $Y=\int_{\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt, \text{ where } \phi \left ( t \right )=\begin{cases} 1; & 5\leq t\leq 7 &\\ 0; & \text{otherwise} \end{cases}$ and $W(t)$ is a real white Gaussian noise process with twosided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.
asked
Feb 13
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by
jothee
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1.4k
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gate2020ec
numericalanswers
vectoranalysis
engineeringmathematics
gaussstheorem
0
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0
answers
3
GATE2016327
If the vectors $e_1=(1,0,2)$, $e_2=(0,1,0)$ and $e_3=(2,0,1)$ form an orthogonal basis of the threedimensional real space $\mathbb{R}^3$, then the vector $\textbf{u}=(4,3,3)\in \mathbb{R}^3 $ can be expressed as $\textbf{u}=$\large\frac{2}{5}$e_13e_2$\ ... $e_1+3e_2+$\large\frac{11}{5}$e_3 \\$ $\textbf{u}=$\large\frac{2}{5}$e_1+3e_2$\large\frac{11}{5}$e_3$
asked
Mar 28, 2018
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by
Milicevic3306
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15.7k
points)
gate2016ec3
vectoranalysis
engineeringmathematics
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0
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4
GATE2016350
A voicegrade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of $4.0\:kHz$ and twosided noise power spectral density ${\large\frac{\eta}{2}}=2.5\times10^{5}Watt\:per\:Hz$. If information at the rate of $52\:kbps$ is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bitenergy $E_b$ (in mJ/bit) necessary is _______
asked
Mar 28, 2018
in
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by
Milicevic3306
(
15.7k
points)
gate2016ec3
numericalanswers
vectoranalysis
gauss'stheorem
engineeringmathematics
0
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0
answers
5
GATE201625
Consider the timevarying vector $\textbf{I}=\hat{x}15\cos(\omega t)+\hat{y}5\sin(\omega t)$ in Cartesian coordinates, where $\omega> 0$ is a constant. When the vector magnitude $\mid \textbf{I} \mid$ is at its minimum value, the angle $\theta$ that $\textbf{I}$ makes with the $x$ axis (in degrees, such that $ 0\leq \theta \leq 180)$ ________
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Mar 28, 2018
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Milicevic3306
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15.7k
points)
gate2016ec2
numericalanswers
vectoranalysis
engineeringmathematics
0
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0
answers
6
GATE2016255
A positive charge $q$ is placed at $x=0$ between two infinte metal plates placed at $x=d$ and at $x=+d$ respectively. The metal plates lie in the $yz$ plane. The charge is at rest at $t=0$, when a voltage $+V$ is applied to the plate at $d$ and voltage $V$ is ... time that the charge $q$ takes to reach the right plate is proportional to $d/V$ $\sqrt{d}/V$ $d/\sqrt{V}$ $\sqrt{d/V}$
asked
Mar 28, 2018
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by
Milicevic3306
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15.7k
points)
gate2016ec2
vectoranalysis
0
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0
answers
7
GATE2016150
An analog pulse $s(t)$ is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is $r(t) = s(t) + n(t)$, where $n(t)$ is additive white Gaussian noise with power spectral density $\frac{N_0}{2}$. The received signal is passed through a filter with ... $E_s > E_h$ ; $SNR_{max}>\frac{2E_s}{N_0} \\ $ $E_s < E_h$ ; $SNR_{max}=\frac{2E_h}{N_0}$
asked
Mar 28, 2018
in
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by
Milicevic3306
(
15.7k
points)
gate2016ec1
vectoranalysis
engineeringmathematics
gauss'stheorem
0
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0
answers
8
GATE2015329
A vector field $\textbf{D} = 2\rho^{2}\:\textbf{a}_{\rho} + z\: \textbf{a}_{z}$ exists inside a cylindrical region enclosed by the surfaces $\rho =1,z = 0$ and $z = 5.$ Let $S$ be the surface bounding this cylindrical region. The surface integral of this field on $S(∯_{S} \textbf{D.ds})$ is _______.
asked
Mar 28, 2018
in
Others
by
Milicevic3306
(
15.7k
points)
gate2015ec3
numericalanswers
vectoranalysis
engineeringmathematics
0
votes
0
answers
9
GATE2015249
A zero mean white Gaussian noise having power spectral density $\dfrac{N_{0}}{2}$ is passed through an LTI filter whose impulse response $h(t)$ is shown in the figure. The variance of the filtered noise at $t = 4$ is $\dfrac{3}{2}A^{2}N_{0} \\$ $\dfrac{3}{4}A^{2}N_{0} \\$ $A^{2}N_{0} \\$ $\dfrac{1}{2}A^{2}N_{0}$
asked
Mar 28, 2018
in
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by
Milicevic3306
(
15.7k
points)
gate2015ec2
vectoranalysis
engineeringmathematics
gauss'stheorem
0
votes
0
answers
10
GATE2015154
The electric field intensity of a plane wave traveling in free space is given by the following expression $\textbf{E}(x,t)=\textbf{a}_y \: 24 \: \pi \: \: \cos(\omega t – k_0 x) \: \: (V/m)$ In this field, consider a square area $10 \: \text{cm} \times 10 \: \text{cm}$ on a plane $x+y=1$. The total timeaveraged power (in mW) passing through the square area is _____________.
asked
Mar 28, 2018
in
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by
Milicevic3306
(
15.7k
points)
gate2015ec1
numericalanswers
vectoranalysis
0
votes
0
answers
11
GATE2015155
Consider a uniform plane wave with amplitude $(E_0)$ of $10 \: V/m$ and $1.1$ GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $(\varepsilon _r)$ and permeability $(\mu _r)$ as ... transmitted electric field component (in V/m) after it has travelled a distance of $10$ cm inside the dielectric region is ____________.
asked
Mar 28, 2018
in
Others
by
Milicevic3306
(
15.7k
points)
gate2015ec1
numericalanswers
vectoranalysis
0
votes
0
answers
12
GATE201442
The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.
asked
Mar 26, 2018
in
Others
by
Milicevic3306
(
15.7k
points)
gate2014ec4
numericalanswers
vectoranalysis
engineeringmathematics
gradient
0
votes
0
answers
13
GATE201443
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
asked
Mar 26, 2018
in
Others
by
Milicevic3306
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15.7k
points)
gate2014ec4
numericalanswers
vectoranalysis
engineeringmathematics
gauss'stheorem
0
votes
0
answers
14
GATE2014422
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be Poisson Gaussian Exponential Gamma
asked
Mar 26, 2018
in
Others
by
Milicevic3306
(
15.7k
points)
gate2014ec4
vectoranalysis
gauss'stheorem
0
votes
0
answers
15
GATE2014449
Consider a communication scheme where the binary valued signal $X$ satisfies $P\{X=+1\}=0.75$ and $P\{X=1 \}=0.25$. The received signal $Y=X+Z$, where $Z$ ... $\tau$ should be strictly positive zero strictly negative strictly positive, zero, or strictly negative depending on the nonzero value of $\sigma ^2$
asked
Mar 26, 2018
in
Others
by
Milicevic3306
(
15.7k
points)
gate2014ec4
vectoranalysis
engineeringmathematics
gauss'stheorem
0
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0
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16
GATE2014452
Consider a discretetime channel $Y=X +Z$, where the additive noise $Z$ is signaldependent. In particular, given the transmitted symbol $ X \in \{a , +a\}$ at any instant, the noise sample $Z$ is chosen independently from a Gaussian distribution with mean $\beta X$ and unit variance. Assume a ... $\beta = 0.3$, the BER is closest to $10^{7}$ $10^{6}$ $10^{4}$ $10^{2}$
asked
Mar 26, 2018
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by
Milicevic3306
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15.7k
points)
gate2014ec4
vectoranalysis
engineeringmathematics
gauss'stheorem
0
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0
answers
17
GATE2014353
Given the vector $\textbf{A}= ( \cos x ) ( \sin y )\hat{a_{x}}+( \sin x )( \cos y )\hat{a_{y}},$ where $\hat{a_{x}},$ $\hat{a_{y}}$ denote unit vectors along $x$, $y$ directions, respectively. The magnitude of curl of $\textbf{A}$ is __________
asked
Mar 26, 2018
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Milicevic3306
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15.7k
points)
gate2014ec3
numericalanswers
vectoranalysis
engineeringmathematics
0
votes
0
answers
18
GATE2014222
The capacity of a bandlimited additive white Gaussian noise (AWGN) channel is given by $C = W \log_{2}\left ( 1+\frac{p} {\sigma ^{2}w} \right )$ bits per second (bps), where $W$ is the channel bandwidth, $P$ ... $(W\rightarrow \infty )$ is approximately $1.44$ $1.08$ $0.72$ $0.36$
asked
Mar 26, 2018
in
Others
by
Milicevic3306
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15.7k
points)
gate2014ec2
vectoranalysis
gauss'stheorem
0
votes
0
answers
19
GATE201413
$C$ is a closed path in the $z$plane given by $\mid z \mid = 3.$ The value of the integral $\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}z+4j}{z+2j}\bigg)dz$ is $4\pi(1+j2)$ $4\pi(3j2)$ $4\pi(3+j2)$ $4\pi(1j2)$
asked
Mar 26, 2018
in
Others
by
Milicevic3306
(
15.7k
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gate2014ec1
vectoranalysis
0
votes
0
answers
20
GATE2014128
The volume under the surface $z(x,y) = x + y$ and above the triangle in the $x – y$ plane defined by $\{0 \leq y \leq x \: \text{and} \: 0 \leq x \leq 12\}$ is _______.
asked
Mar 26, 2018
in
Others
by
Milicevic3306
(
15.7k
points)
gate2014ec1
numericalanswers
vectoranalysis
0
votes
0
answers
21
GATE2014146
Consider the state space model of a system, as given below ... The system is controllable and observable uncontrollable and observable uncontrollable and unobservable controllable and unobservable
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Mar 26, 2018
in
Others
by
Milicevic3306
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15.7k
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gate2014ec1
vectoranalysis
0
votes
0
answers
22
GATE2014153
In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions. $\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omega t  \beta r)\hat{a_{\theta}}\: V/m$ ... antenna, in free space. The average power $(W)$ crossing the hemispherical shell located at $r = 1\:km,0\leq \theta \leq \pi/2$ is ______.
asked
Mar 26, 2018
in
Others
by
Milicevic3306
(
15.7k
points)
gate2014ec1
numericalanswers
vectoranalysis
0
votes
0
answers
23
GATE201352
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ denote incident, reflected, and transmitted electric field vectors associated with the wave. The angle of incidence $\theta_{i}$ and ...
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Mar 26, 2018
in
Others
by
Milicevic3306
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15.7k
points)
gate2013ec
vectoranalysis
0
votes
0
answers
24
GATE201353
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ denote incident, reflected, and transmitted electric field vectors associated with the wave. The expression for $\vec{E_{r}}$ ...
asked
Mar 26, 2018
in
Others
by
Milicevic3306
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15.7k
points)
gate2013ec
vectoranalysis
0
votes
0
answers
25
GATE201339
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ ... $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}$
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Mar 26, 2018
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Others
by
Milicevic3306
(
15.7k
points)
gate2013ec
vectoranalysis
0
votes
0
answers
26
GATE20137
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$ $1/3$ $1$ $3$
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Mar 26, 2018
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Others
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Milicevic3306
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15.7k
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gate2013ec
vectoranalysis
0
votes
0
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27
GATE20132
Consider a vector field $\vec{A}(\vec{r}).$ The closed loop line integral $\displaystyle {} \int \vec{A}\bullet\vec{dl}$ can be expressed as $\displaystyle {} \iint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the closed surface bounded by the ... bounded by the loop $\displaystyle {} \iiint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the open surface bounded by the loop
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2013ec
vectoranalysis
0
votes
0
answers
28
GATE201223
Given $f(z)=\frac{1}{z+1}\frac{2}{z+3}$. If $C$ is a counterclockwise path in the zplane such that $\mid z+1 \mid=1$, the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is $2$ $1$ $1$ $2$
asked
Mar 25, 2018
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Others
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Milicevic3306
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15.7k
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gate2012ec
vectoranalysis
engineeringmathematics
0
votes
0
answers
29
GATE2017 EC2: 28
If the vector function $\overrightarrow{F}=\widehat{a_x}(3yk_1z)+\widehat{a_y}(k_2x2z)\widehat{a_z}(k_3y+z)$ is irrotational, then the values of the constants $k_1$,$k_2$ and $k_3$, respectively, are $0.3, 2.5, 0.5$ $0.0, 3.0, 2.0$ $0.3, 0.33, 0.5$ $4.0, 3.0, 2.0$
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec2
vectoranalysis
overrightarrow
engineeringmathematics
0
votes
0
answers
30
GATE2017 EC2: 3
The smaller angle (in degrees) between the planes $x+y+z=1$ and $2xy+2z=0$ is ________.
asked
Nov 23, 2017
in
Vector Analysis
by
admin
(
2.8k
points)
gate2017ec2
vectorinplanes
numericalanswers
vectoranalysis
0
votes
0
answers
31
GATE2017 EC1: 28
Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,1)$.The value of $I$ is ____________.
asked
Nov 17, 2017
in
Vector Analysis
by
admin
(
2.8k
points)
gate2017ec1
numericalanswers
vectoranalysis
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